Solid State Kinetic Parameters and Chemical Mechanism of the Dehydration of CoCI2-6H20 An Inorganic Solid State Experiment Joan Rlbasl, Albert Escuer, Miquel Serra, and Ramon Vicente Universitat de Barcelona, Diagonal 647, 08028-Barcelona, Spain In the past several years, there has been agrowing interest in the determination of kinetic and thermodynamic parameters from solid state reactions in order to establish the reaction mechanisms (I). In this article are presented descriptions of (1) an experimental example illustrating the most common methods for the determination of kinetic parameters, (2) the different theories and equations to he applied, and (3) the discussion of the mechanism derived from the kinetic results. The exoerimental examnle chosen is the solid state dehvdration reaction of COC~$H~O.This substance is inexpensive and is not dangerous. I t is regularly used in humidity detectors in its anhydrous form. Additionally, all the intermediate products have a known structure. This fact will permit discussion relating the kinetic and structural parameters. Experlmentai Thermogravimetric (TG) analyses were carried out under nitrogen (10 mllmin), on a Perkin-Elmer model TGS-1 system. The sample size being in the range 4-7 mg. The heating rate for nonisothermal experiments was 5 'Clmin. The heating rate to arrive at the work temperature in the isothermal TG was 40 OCImin. The DSC studies were carried out using a DSC-2 PerkinElmer Differential Scanning Calorimeter under the same conditions as TG studies. The value of AH was calculated from the area of the DSC peak, using Sn and In for calihration (2). Theoretlcai Background for Solld State Kinetics The general expression employed (3)in the determination of the solid state kinetic parameters is
where a is themolar fraction of the reacted product a t a time t, g(a) is the expression of the physical model according to which the solid state reaction is assumed to occur, and k(T) is the rate constant of the process, related to the activation energy, E., according to the Arrhenius expression, k ( T ) = k, exp(-EJRT)
(2)
The main expressions of g(a) are presented in Table 1 (I, 4). These expressions have been deduced from solid state physics, taking into account the formation of nuclei and their growth at the interface in one, two, or three directions, and their shapes (cylindrical, spherical, etc.) (I). Calculation of E. from TO Dlagrams Initially i t is necessary to do a dynamic TG with a linear variation of the temperature. This dynamic T G affords the temperature range in which the reaction takes place. In
' Auihor to whom correspondenceshould be addressed.
Table 1. Algebraic Functions g ( m ) and thelr Abbrevlatlons Used in the Analysis of Isothermal TO Curves Mechanism
s(a)
Nucleafion controlled Power law
RI
GTDwth ont trolled for n = 1 Nucleation-Growth controlled Avrami-Eroleev Diffusion controlled Onedimensional Twodimensional Threedimensional Threedimensional
Abbrev.
[I - (1 - a)'-"] [-in (1- a)] [-in (1
- a)]""
a2 a (1 a)In (1 a) [l (1 a)'/3]2 (1 - 213 a) (1
+ -
- - -
RI. RB FI A?. A?
DI D2 D3
D4
order to obtain meaningful kinetic parameters from the central interval of this dynamic-TG curve, it is necessary to record data for five or six isothermal runs with a 2-3 OC separation between each TG run. With these isothermal runs, the integration of eq 1 is immediate since k(T) is not a function of t. The final expression is g(a) = k(T)t. It is necessary to take only the experimental points between a = 0.2 and a = 0.8. By representing g(a) vs. t the rate constants for each temperature and model are ohtained. Applying the Arrhenius equation i t is possible to obtain E, directly as the slope of the resulting in [k(T)]vs. 11T. In this way, an E, value practically independent of the applied g(a) is ohtained (5). Recently one of the authors (6) has shown that the activation energy is not only independent of g(a) hut can he easily calculated with the aid of a pocket calculator from the expression In (At) = E,IRT+ ct
(3)
where At is the time increment between the point corresuondina to a = 0.2-0.8 and T is the isothermal temoerature. The slope ohtained by linear regression of the plot k i n (At) vs. 1IT is E.IR. Calculation of the Actlvatlon Entropy If the rate constants at each temperature are known, AS$ can he easily calculated by means of the Eyring equation, In (k,hlkBT) = ASt/R - AHt/RT
(4)
The intercept ohtained by linear regression of in (kohlkaT) vs. 1/T, gives AS%. Reaction Mechanism In the field of kinetics and mechanisms of coordination compounds in the solid state, a small amount of literature data is found. House (7) proposed in 1980 the first theory of thermal reactions in solid complexes. According to this theory, a general mechanism is proposed Volume 65 Number 1 January 1988
85
the next units. This oroduces a souare of chloride ions around earhCorllJ ionand linksallthecentral metal ions intoapolymrrir structure along the b axis with thr chloride ions acting as the linking ions. (See Fig. 1(12).)The AH. calculated by DSC measurements is 82 kJ/mol, (-20 kJ/mol HzO). The activation energy of the first Drocess is verv low. The loss of the first two water mole&les leaves thelattice structure relatively the same; the loss of the second oair of water molecules (coordination water), is very easy because the structure is "open", due to the simultaneous loss of crystallization water. Therefore, there is in the lattice substantial free space, readily facilitating the escape of these water molecules.
+
CoC/pZH20(s) CoCIpH20(s) Hzqg) The value of AHbis 20 kJ/mol, practically equal to that for one mol of Hz0 in the previous case. The CoClrH20 has a very similar structure to the previous CoC122H20 with a difference due to the loss of one molecule of water, which gives a two-dimensional structure in which each Co(I1) is octahedrally surrounded by four shared chlorides and by two shared water molecules (in trans positions) (Fig. 1).The activation energy of this process is relatively high, (-91 kJ/ mol). It is a process in which one of the water molecules (coordination-water) is lost to give a two-dimensional rtructure in which the chlorides and water molecules are shared. The freespace between each chain is minimal. +
Figure 1. NonlsothermalTO curve forCoClz6H20wlth the Idealized structures of the corresponding CoC1p2H20 and CoClrHP.
in terms of a "defect-diffusion" model in which the forma~-~~ tion of point defects is equivalent to the transition state. Followine the cwstal field armments of Basolo and Pearson (a), ~ o u l assukes e that in t i e formation of the intermediate, the Dq parameter contributes fundamentally in solid state reactions. In the last several years an attempt has been made to generalize this theory (9).Therefore, new amine complexes of Co(II1). CdIII), Rh(III), and Ir(II1) have been studied systematically varying the entering anion and the sire of the coordinated amines. Although the derived E, can be correlated with the crystal field activation energy (CFAE), all the experimental values with Rh(lll) and ir(ll1J and many examnlrs withCrllll~withcertainamioesarelower than those c a l k a t e d withthd CFAE only. This trend lends credence to the imnortance of the "free s ~ a c e "concept already defined by ~o;se; that is, to assume that E, depends n& only on CFAE hut also. and soeciallv, on the variation in size of the ions or the free'spaceieft fo; the ions in the lattice. ~
~~~
~~
~
--
+
CoC/&) Hmg) CoC/pH2qs) The value of AH, is very high (98.1 kJ/mol), almost five times greater than AH for the previous reactions. This high
Results and Dlscusslon T h e e q u i l i b r i u m t h e r m a l decomposition of t h e CoC126Hz0 was studied through the temperature range 293-473 K by means of DSC and TG. ThenonisothermalTG curve for CoC126Hz0 is given in Figure 1. The observed reaction occurs in three stages which are discussed below, and whose thermodynamic and kinetic parameters are given in Table 2.
-
+
CoCIpZHzqs) 4 H N g ) CoCIpGH20(s) In the hexahydrate, two molecules of water are external to the [COCI~.(H~O)~] inner coordination sphere ( 1 0 , l l ) . The loss of the two crystallization and two coordinated water molecules is practically simultaneous. According to Grindstaff and co-workers (10). Theloss of the second pair of water molecules has the same energy as the loss of the first pair, although the second pair must be from the inner coordination sohere. We can understand the loss of the two coordinated water molerulcs if the chloride ions oi thr two adjacenta unrts of ICoC12(H20,,I replare the uater molrculr in ~~
~
Figure 2. Energetic diagram for the dehydration of CaCI..6H20
Table 2. Klnetlc Parameters lor the Three Stages in the Thermal Deaquation ol CoClp.6H20(s)
--
CoCbBHP(s) CaCI2.2H~0(s) + 4H20(g) CoCI,.WP(s) CcCl&O(s) + H20(g) CoC1rHzO(s) COCI&) + H20(g) 86
Journal of Chemical Education
AH(kJImo1) 82 i 2 20 i 2 98 i 4
E,
(kJImo1)
In ko
42i3 91i5 57 i 3
13.9 27.5 14.7
A S (cal/mol.K)
-33
i6 -6+2 -32 i 5
value can he understood taking into account the structures of CoClyH20 (Fig. 1) and anhydrous CoC12, which has the CdCl2 structure. The total energy necessary to effect the rearrangement of the monohydrate to anhydrous CoClz explains the high AH value, hut simultaneously this rearrangement leaves many tunnels by which the water molecule can easily escape. The activation energy must he low (Table 2). Furthermore, the A S calculated from eq 4, also may indicate the differences between the steps of the dehydration (Table 2). According to House (7),the entropy effect may also he explained by the relative sizes (in our case the relative packing) of the ions and the free volume; where there is a large space between the ions (as we suppose in the first and third steps), the water molecule may he able to slip into an interstitial position causing little or no lattice distortion. Therefore the entropy of activation may he negative. Where there is a smaller space between the ions (as we can suppose in the second step), the water molecules can occupy an interstitial position only with considerable lattice expansion so that the entrow of activation is less neaative or positive ~ h entropy reasoning of ~ o u s L i specs (Tahle 2). ~ l t h b i this ulative, we believe that i t gives an intuitive comprehension of the process.
Conclusions The energetic diagram of the dehydration-anation of the CoCl2.6H20 is represented in Figure 2. This diagram explains that the most stable species is CoC12.2Hz0. In the TG curve (Fig. 1) this fact may he clearly seen; i t is the species which exists in the greatest temperature interval. On the other hand, once the activation energy for the dihydrate is surpassed, CoClyH20 and CoC12 are rapidly formed and the temperature interval separating them is very low. Literature Clted e H.;Tipper, C. F. H., 1. Dollimore, H. In C o m p r e h e ~ i vChomieoiKinelics:Bamford.C. Eda.; Elsevier: New York. 1977: Val. 22. Chanter 3. 2. ~ ~ ~ & h t oJ.n L.; , MO&.~, C. T ~iffDIdnti.d scanning ~ ~ ~perkin-~ Elmer: ConnKtiml 3. Y0ung.D. A.DecomposilionafSolids:Pergamon:Ofird.l966:Chapter 1:Garncr.W. E.. TheChomisL~yof th~SolidSLols:ButtamorU1:London, 1955:Chapter J;Zsako, J. J. Thermal Anol. 1973.5.239. 4. Haneak. J. D.: Sharp. J. ~ :Am.iCeromie Sm. 1972.55.78. 5. Criado. J. M.; Gonzalpz, M.; Ortee,, A.: Real, C. J Thermal Anol. 1984.29.243 .. -. .. ..,... .... . ... ..............,..... .. .... 7. House. J.E. Tharmoehim.Acf~1980.38.59. 8. Basolo, F.;Pearson, R. G . Mechanism of Inorganic Renctiona, 2nd 4.:Wiley: New
."...,
""4,w"."m ."",,y",.
9. Ribas, J.; Serra, M.; Escuer. A. Inerg Chem. 1984.23, 2336 and references therein; Ribas. J.; Eseuer A,: Monfort, M. Inorg. Chern. 1985, 24. 1874 and referencez therein. 10. GrindstafS W K.; F w d , N. J. Chem. Sm. Dalton 1972.1477. 11. Mizumo, J. J. Phys. Sac. Jopon I960.25.1412. 12. Morosin. B.; Gmober, E. 3. Acta Cryst. 1%3,16,1176.
Volume 65 Number 1 January 1988
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